Without more details, including photos of each switch, it's difficult to know exactly how your system is wired.
In the photo you've posted there are 4 wires, but two of them are connected to the same terminal on the switch. In the switch that has 4 grey wires, do these connect to four different terminals on the switch, or are some of them connected into the same terminal on the switch?
You should take a look at this website:
https://en.m.wikipedia.org/wiki/Multiway_switchingCompare your wiring to the various diagrams - my guess is that you have a variation on the "Traveller" system - and see if it helps you make more sense of the wiring.
You really need a test meter and a length of wire to allow you to trace which wire is which (with the power off and the the wires disconnected from the switches. You'll need to label each wire first so you know how they are wired at the moment.
Grey wires are generally used to identify the switched live. If you look at the light fitting in the ceiling you'll probably find a neutral (blue or black) and a switched live (grey) wire. The grey will connect back to one of the switches and one of the switched will have a live feed (probably brown).
Pete.